Use the graph of f to calculate . PLEASE HELP!

You should already be aware that the definite integral of is equivalent to the signed area under the curve of

corresponds the area of the triangle on the left, and

is the area of the trapezoid in the middle. You should know how to compute the area of these shapes.

We end up with

since the triangle has height 2 and base 1, and the trapezoid has height 2 with two base lengths 1 and 3.

Edit: The area under the curve is highlighted red in the attachment below. It's the area between the curve and the horizontal axis, but it's also signed, meaning the area below the axis is negative, and the area above the axis is positive.

step-by-step explanation:

the shape,the size and the distance

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!